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解答 - 几何数列

公比是：

r = 0.631578947368421

r=0.631578947368421

该系列的和是：

s = 155

s=155

此系列的通用形式是：

a_{n} = 95 \cdot {0.631578947368421}^{n - 1}

a_n=95*0.631578947368421^(n-1)

这个序列的第n项是：

95, 60, 37.89473684210526, 23.933518005540165, 15.115906108762207, 9.546888068691919, 6.02961351706858, 3.808176958148577, 2.4051643946201535, 1.5190511966022022

95,60,37.89473684210526,23.933518005540165,15.115906108762207,9.546888068691919,6.02961351706858,3.808176958148577,2.4051643946201535,1.5190511966022022

查看步骤

逐步解答

1. 找到公比

通过将序列中的任何项除以前一项来找到公比：

$a_{2} a_{1} = \frac{60}{95} = 0.631578947368421$

该序列的公比（ $r$ ）保持不变，并且等于两个连续项的商。
$r = 0.631578947368421$

2. 求和

5 个额外步骤

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

要找到系列的和，将第一项： $a = 95$ 、公比： $r = 0.631578947368421$ 和元素数目 $n = 2$ 插入几何级数求和公式：

$s_{2} = 95 * ((1 - {0.631578947368421}^{2}) / (1 - 0.631578947368421))$

$s_{2} = 95 * ((1 - 0.39889196675900274) / (1 - 0.631578947368421))$

$s_{2} = 95 * (0.6011080332409973 / (1 - 0.631578947368421))$

$s_{2} = 95 * (0.6011080332409973 / 0.368421052631579)$

$s_{2} = 95 \cdot 1.631578947368421$

$s_{2} = 155$

3. 找到通用形式

$a_{n} = a \cdot r^{n - 1}$

要找到系列的通用形式，将第一项： $a = 95$ 和公比： $r = 0.631578947368421$ 插入几何级数的公式：

$a_{n} = 95 \cdot {0.631578947368421}^{n - 1}$

4. 找到第n项

使用通用公式找到第n项

$a_{1} = 95$

$a_{2} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{2 - 1} = 95 \cdot {0.631578947368421}^{1} = 95 \cdot 0.631578947368421 = 60$

$a_{3} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{3 - 1} = 95 \cdot {0.631578947368421}^{2} = 95 \cdot 0.39889196675900274 = 37.89473684210526$

$a_{4} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{4 - 1} = 95 \cdot {0.631578947368421}^{3} = 95 \cdot 0.25193176847937016 = 23.933518005540165$

$a_{5} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{5 - 1} = 95 \cdot {0.631578947368421}^{4} = 95 \cdot 0.15911480114486534 = 15.115906108762207$

$a_{6} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{6 - 1} = 95 \cdot {0.631578947368421}^{5} = 95 \cdot 0.10049355861780968 = 9.546888068691919$

$a_{7} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{7 - 1} = 95 \cdot {0.631578947368421}^{6} = 95 \cdot 0.06346961596914295 = 6.02961351706858$

$a_{8} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{8 - 1} = 95 \cdot {0.631578947368421}^{7} = 95 \cdot 0.04008607324366923 = 3.808176958148577$

$a_{9} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{9 - 1} = 95 \cdot {0.631578947368421}^{8} = 95 \cdot 0.02531751994337004 = 2.4051643946201535$

$a_{10} = a_{1} \cdot r^{n - 1} = 95 \cdot {0.631578947368421}^{10 - 1} = 95 \cdot {0.631578947368421}^{9} = 95 \cdot 0.015990012595812654 = 1.5190511966022022$

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